Non-rigid Shape Registration Using Similarity-Invariant Differential Coordinates

2013 ◽  
Author(s):  
Shuntaro Yamazaki ◽  
Satoshi Kagami ◽  
Masaaki Mochimaru
Keyword(s):  
Shape Registration ◽  
Differential Coordinates ◽  
Invariant Differential ◽  
Similarity Invariant

scholarly journals Differential-algebraic systems are generically controllable and stabilizable

2021 ◽  
Author(s):  
Achim Ilchmann ◽  
Jonas Kirchhoff
Keyword(s):  
Algebraic Geometry ◽  
Linear Time ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Algebraic Systems ◽  
Linear Time Invariant ◽  
Survey Article ◽  
Link Type ◽  
Invariant Differential ◽  
Time Invariant

AbstractWe investigate genericity of various controllability and stabilizability concepts of linear, time-invariant differential-algebraic systems. Based on well-known algebraic characterizations of these concepts (see the survey article by Berger and Reis (in: Ilchmann A, Reis T (eds) Surveys in differential-algebraic equations I, Differential-Algebraic Equations Forum, Springer, Berlin, pp 1–61. 10.1007/978-3-642-34928-7_1)), we use tools from algebraic geometry to characterize genericity of controllability and stabilizability in terms of matrix formats.

scholarly journals A construction of the general relativistic Boltzmann equation

1984 ◽  
Vol 7 (3) ◽  
pp. 591-597 ◽  
Author(s):  
P. Dolan ◽  
A. C. Zenios
Keyword(s):  
Distribution Function ◽  
Boltzmann Equation ◽  
Kinetic Equation ◽  
Simple Model ◽  
State Space ◽  
Differential Forms ◽  
Relativistic Boltzmann Equation ◽  
Dimensional State Space ◽  
General Relativistic ◽  
Invariant Differential

Our work depends essentially on the notion of a one-particle seven-dimensional state-space. In constructing a general relativistic theory we assume that all measurable quantities arise from invariant differential forms. In this paper, we study only the case when instantaneous, binary, elastic collisions occur between the particles of the gas. With a simple model for colliding particles and their collisions, we derive the kinetic equation, which gives the change of the distribution function along flows in state-space.

A GPU-based elastic shape registration approach in implicit spaces

2017 ◽  
Vol 16 (6) ◽  
pp. 2059-2071
Author(s):  
Ahmed Hassan Yousef ◽  
Hossam E. Abd El Munim
Keyword(s):  
Shape Registration

scholarly journals Shape Registration with Learned Deformations for 3D Shape Reconstruction from Sparse and Incomplete Point Clouds

2021 ◽  
pp. 102228
Author(s):  
Xiang Chen ◽  
Nishant Ravikumar ◽  
Yan Xia ◽  
Rahman Attar ◽  
Andres Diaz-Pinto ◽  
...  
Keyword(s):  
Point Clouds ◽  
Shape Reconstruction ◽  
3D Shape ◽  
Shape Registration ◽  
3D Shape Reconstruction

scholarly journals V4PCS: Volumetric 4PCS Algorithm for Global Registration

2017 ◽  
Author(s):  
Jida Huang ◽  
Tsz-Ho Kwok ◽  
Chi Zhou
Keyword(s):  
Mass Customization ◽  
Process Development ◽  
Three Dimensional ◽  
Rigid Transformation ◽  
New Paradigm ◽  
Shape Registration ◽  
Related Data ◽  
Global Registration ◽  
Information Reuse ◽  
Customized Products

With the advances in hardware and process development, additive manufacturing is realizing a new paradigm: mass customization. There are massive human-related data in mass customization, but there are also many similarities in mass-customized products. Therefore, reusing information can facilitate mass customization and create unprecedented opportunities in advancing the theory, method, and practice of design for mass-customized products. To enable information reuse, different models have to be aligned so that their similarity can be identified. This alignment is commonly known as the global registration that finds an optimal rigid transformation to align two three-dimensional shapes (scene and model) without any assumptions on their initial positions. The Super 4-Points Congruent Sets (S4PCS) is a popular algorithm used for this shape registration. While S4PCS performs the registration using a set of 4 coplanar points, we find that incorporating the volumetric information of the models can improve the robustness and the efficiency of the algorithm, which are particularly important for mass customization. In this paper, we propose a novel algorithm, Volumetric 4PCS (V4PCS), to extend the 4 coplanar points to non-coplanar ones for global registration, and theoretically demonstrate the computational complexity is significantly reduced. Several typical human-centered applications such as tooth aligner and hearing aid are investigated and compared with S4PCS. The experimental results show that the proposed V4PCS can achieve a maximum of 20 times speedup and can successfully compute the valid transformation with very limited number of sample points.

Similarity-invariant signatures for partially occluded planar shapes

1992 ◽  
Vol 7 (3) ◽  
pp. 271-285 ◽  
Author(s):  
Alfred M. Bruckstein ◽  
Nir Katzir ◽  
Michael Lindenbaum ◽  
Moshe Porat
Keyword(s):  
Invariant Signatures ◽  
Planar Shapes ◽  
Similarity Invariant ◽  
Partially Occluded
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